Question

Use the table to answer the question. House A $124,270 Annual appreciation 4% House B $114,270 Annual appreciation 5% In which of these years after it was purchased is the value of House A greater than the value of House B? Check all that apply. 7 8 9 10

Answer 1

For the house A we have:
 f (x) = 124270 (1.04) ^ x
 Evaluating for 7, 8, 9 and 10 we have:
 f (7) = 124270 (1.04) ^ 7 = 163530.8422
 f (8) = 124270 (1.04) ^ 8 = 170072.0759
 f (9) = 124270 (1.04) ^ 9 = 176874.9589
 f (10) = 124270 (1.04) ^ 10 = 183949.9573

 For house B we have:
 f (x) = 114270 (1.05) ^ x
 Evaluating for 7, 8, 9 and 10 we have:
 f (7) = 114270 (1.05) ^ 7 = 160789.3653
 f (8) = 114270 (1.05) ^ 8 = 168828.8336
 f (9) = 114270 (1.05) ^ 9 = 177270.2752
 f (10) = 114270 (1.05) ^ 10 = 186133.789

 We observe that for years 7 and 8 the value of house A is greater than the value of house B.

 Answer:
 7 and 8